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We introduce a novel approach to study neurons as sophisticated I/O information processing units by utilizing recent advances in the field of machine learning. We trained deep neural networks (DNNs) to mimic the I/O behavior of a detailed nonlinear model of a layer 5 cortical pyramidal cell, receiving rich spatio-temporal patterns of input synapse activations. A Temporally Convolutional DNN (TCN) with seven layers was required to accurately, and very efficiently, capture the I/O of this neuron at the millisecond resolution. This complexity primarily arises from local NMDA-based nonlinear dendritic conductances. The weight matrices of the DNN provide new insights into the I/O function of cortical pyramidal neurons, and the approach presented can provide a systematic characterization of the functional complexity of different neuron types. Our results demonstrate that cortical neurons can be conceptualized as multi-layered "deep" processing units, implying that the cortical networks they form have a non-classical architecture and are potentially more computationally powerful than previously assumed. Compartmental model; Dendritic nonlinearitiesNeurons are the computational building blocks of the brain. Understanding their input-output (I/O) transformation has therefore been a major quest in neuroscience since Ramon y Cajal's "neuron doctrine". With the recent development of sophisticated genetical, optical and electrical techniques it has become clear that many key neuron types (e.g., cortical and hippocampal pyramidal neurons, cerebellar Purkinje cells) are highly complicated I/O information processing devices. They receive a barrage of thousands of synaptic inputs via their elaborated dendritic branches; these inputs interact with a plethora of local nonlinear regenerative processes, including the back-propagating (Na + -dependent) action potential (G. J. Stuart and Sakmann 1994), the multiple local dendritic NMDA-dependent spikes (Polsky, Mel, and Schiller 2004;Branco, Clark, and Häusser 2010; Kastellakis et al. 2015), and the large and prolonged Ca 2+ spike at the apical dendrite of L5 cortical pyramidal neurons (M E Larkum, Zhu, and Sakmann 1999). As a result of local nonlinear dendritic processing, a train of output spikes are generated in the neuron axon, carrying information that is communicated, via synapses, to thousands of other (postsynaptic) neurons. Indeed, as a consequence of their inherent nonlinear mechanisms, neurons can implement highly complicated I/O functions (

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A cortical neuron typically makes multiple synaptic contacts on the dendrites of a post-synaptic target neuron. The functional implications of this apparent redundancy are unclear. The dendritic location of a synaptic contact affects the time-course of the somatic post-synaptic potential (PSP) due to dendritic cable filtering. Consequently, a single pre-synaptic axonal spike results with a PSP composed of multiple temporal profiles. Here, we developed a "filter-and-fire" (F&F) neuron model that captures these features and show that the memory capacity of this neuron is threefold larger than that of a leaky integrate-and-fire (I&F) neuron, when trained to emit precisely timed output spikes for specific input patterns. Furthermore, the F&F neuron can learn to recognize spatio-temporal input patterns, e.g., MNIST digits, where the I&F model completely fails. Multiple synaptic contacts between pairs of cortical neurons are therefore an important feature rather than a bug and can serve to reduce axonal wiring requirements.

Dynamic changes in sensory representations have been basic tenants of studies in neural coding and plasticity. In olfaction, relatively little is known about the dynamic range of changes in odor representations under different brain states and over time. Here, we used time-lapse in vivo two-photon calcium imaging to describe changes in odor representation by mitral cells, the output neurons of the mouse olfactory bulb. Using anesthetics as a gross manipulation to switch between different brain states (wakefulness and under anesthesia), we found that odor representations by mitral cells undergo significant re-shaping across states but not over time within state. Odor representations were well balanced across the population in the awake state yet highly diverse under anesthesia. To evaluate differences in odor representation across states, we used linear classifiers to decode odor identity in one state based on training data from the other state. Decoding across states resulted in nearly chance-level accuracy. In contrast, repeating the same procedure for data recorded within the same state but in different time points, showed that time had a rather minor impact on odor representations. Relative to the differences across states, odor representations remained stable over months. Thus, single mitral cells can change dynamically across states but maintain robust representations across months. These findings have implications for sensory coding and plasticity in the mammalian brain.